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A012305
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Expansion of e.g.f. arcsin(arcsin(x)*log(x+1)).
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1
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0, 0, 2, -3, 12, -40, 358, -2499, 25032, -229104, 2865402, -36173115, 550240020, -8500522680, 149846317710, -2762418635235, 56365118364240, -1205267403147360, 27829436319559410, -674568212738977395
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OFFSET
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0,3
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LINKS
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EXAMPLE
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E.g.f. = 2*x^2/2! - 3*x^3/3! + 12*x^4/4! - 40*x^5/5! + ...
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MAPLE
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seq(coeff(series(factorial(n)*arcsin(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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With[{nn=20}, Drop[CoefficientList[Series[ArcSin[ArcSin[x]Log[x+1]], {x, 0, nn}], x] Range[0, nn]!, 2]] (* Harvey P. Dale, Oct 18 2013 *)
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PROG
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(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asin(asin(x)* log(x+1))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arcsin(Arcsin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 25 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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EXTENSIONS
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a(0) and a(1) inserted and title improved by Sean A. Irvine, Jul 17 2018
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STATUS
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approved
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